Question

The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of 2Ω. The value of the internal resistance of each cell is ______.

Options

• 2Ω

• 4Ω

• 6Ω

• 8Ω

Answer 1

The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of 2Ω. The value of the internal resistance of each cell is 2Ω.

Explanation:

Case A: When cells are connected in series, the result is

equivalent EMF, E = 2E

equivalent resistance, r = 2r

And, current, I = `E/(r + R) = (2E)/(2r + 2)`

Case B: Parallel cell connections result in,

equivalent EMF, E = E

equivalent resistance, r = `r/2`

And, current, `I = E/(r + R) = E/(r/2 + 2)`         ...(2)

Because both currents are the same, and thus both equations are equal,

`(2E)/(2r + 2) = E/(r/2 + 2)`

r = 2Ω